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What do you think the graph of 4x+2y=4 looks like? In this lesson you will learn about the graph of this and other similar equations.
Question 2. The slope of a line is a measurement of how steep it is. Use the figures below to help remind you about how to measure the slope of a line. The first line graphed below has slope 32, while the second one has slope −32.
Look at the grid to the left to answer the following questions.
Question 3. To the left is the graph of Ax+By=C. You are looking at the graph of 4x+2y=4 (because A=4, B=2, C=4). Use the sliders to change the values of A, B, and C and notice how each affects the shape and position of the graph of Ax+By=C.
Each row of the following table has a question about how the graph changes when you change A, B, or C. Answer the question for each of the three variables.
The form Ax+By=C, where A, B, and C are constants, is called the standard form for an equation for a line.
Question 4. Use the sliders to set A=4, B=2, and C=4. You are again looking at the graph of 4x+2y=4. Slide the value of A toward zero.
Question 6. Each row of the table below gives an equation for a line in standard form. Using the sliders, change the values of A, B, and C, and complete this table. In each case, find the slope of the line by looking at the grid to the left.
The slopes you have found suggest that:
The slope of the line Ax+By=C is −AB.
In the last question, you found the slopes of lines by looking at their graphs. If you want to find the slope of a line algebraically, by using its equation, you can convert that equation into slope-intercept form.
For example, we can write the equation 4x+2y=4 in slope-intercept form as follows:
Question 7. Each row of the table has an equation in standard form. Write that equation in slope-intercept form.
Question 8. The equations from Question 7 have been summarized in the table below. Use them to answer the following questions.
The y-intercept of a line is the point on that line where x=0, and the x-intercept is the point where y=0. You can use this to find the intercepts of lines algebraically.
Question 9. Algebraically find the y-intercept of each line in the table below.
Question 10. Algebraically find the x-intercept of each line in the table below.